With the advent of advanced computing architectures such as GPUs, many algorithms have required changes in order to properly utilize them. One such approach that is well-suited for GPUs is matrix-free methods. Matrix-free methods can be advantageous over traditional methods due to their memory efficiency and lower computational complexity, but with the cost of needing specialized software frameworks and solvers. Geometric multigrid methods have seen great success on GPU architecture with the regular geometric stencils naturally lending themselves to matrix-free implementations. Algebraic multigrid (AMG) methods are problematic because they usually require information about matrix entries, which may not be easily obtainable in the matrix-free framework. In this talk we discuss the implementation of a matrix-free AMG method in the high-fidelity computational fluid dynamics framework Neko, which utilizes spectral element methods with an implicit-explicit scheme to solve the incompressible Navier-Stokes equations. We utilize an hp-multigrid approach, where the problem is first coarsened from high-order polynomials to low-order polynomials, and then the low-order system is further coarsened spatially in a matrix-free AMG fashion. Leveraging only mesh adjacency information, this algorithm constructs an algebraic multigrid hierarchy without requiring geometric coarsening or explicit matrix assembly, making it well-suited for GPU-accelerated architectures. We present numerical results demonstrating the performance and scalability of our method and applicability to real-world applications.